a) $\left\{\begin{matrix}2x - y = 5\\ 3x + y = 10\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}5x = 15\\ 3x + y = 10\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = 3\\ y = 1\end{matrix}\right.$

b) $\left\{\begin{matrix}x + 5y = 7\\ 3x - 2y = 4\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}2x + 10y = 14\\ 15x - 10y = 20\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}17x = 34\\ x + 5y = 7\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = 2\\ y = 1\end{matrix}\right.$

c) $\left\{\begin{matrix}2x + 5y = -2\\ 3x - 2y = 4\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}4x + 10y = -4\\ 15x - 10y = 20\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}19x = 16\\ 3x - 2y = 4\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}x = \frac{16}{19}\\ y = \frac{-14}{19}\end{matrix}\right.$

d) $\left\{\begin{matrix}3x + 4y = 5\\ 2x - 5y = -12\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}6x + 8y = 10\\ 6x - 15y = -36\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix}23y = 46\\ 3x + 4y = 5\end{matrix}\right.$

$\Leftrightarrow \left\{\begin{matrix} y = 2\\ x = -1\end{matrix}\right.$